#1**0 **

Here's what I tried:

First I looked at 1.75 + sqrt(3) and said, "Well, why not set it equal to a variable?". So I replaced it with x.

Then I got \(2\sqrt{x} - x\), but that didn't help at all. I can't set it equal to anything. I can't solve it with a variable. So then I thought I would just need to solve it by hand. But how in the world would I know what \(\sqrt{3}\) was? Luckily, I remebered that it was 1.732. So, thenI solved it as shown below:

\(2\sqrt{1.75+1.732} - (1.75+1.732)\)

\(=2\sqrt{3.482}-3.482\)

Now what? How do I solve this?

dgfgrafgdfge111 Mar 15, 2019

#5**0 **

If we squared it, though, we would get 2(sqrt(3.482)), which wouldn't simplify.

dgfgrafgdfge111
Mar 15, 2019

#2**0 **

\(2\sqrt{1.75+\sqrt3}-(1.75+\sqrt3)\\ \)

I'm coming up blank.

but sqrt root of 3 is irrational so it is not exactly equal to what you said.

Melody Mar 15, 2019

#8**+2 **

Finally I got it !!

\(2\sqrt{1.75+\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{4(\frac{7}{4}+\sqrt3)}\qquad -(1.75+\sqrt3)\\~\\ =\sqrt{7+4\sqrt3}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2)^2+(2*2*\sqrt3)+(\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =\sqrt{(2+\sqrt3)^2}\qquad-(1.75+\sqrt3)\\~\\ =(2+\sqrt3)\qquad-(1.75+\sqrt3)\\~\\ =2+\sqrt3-1.75-\sqrt3\\~\\ =0.25\)

Is that impressive or what! LOL

Melody Mar 15, 2019